Finite Group DatabasebetaFinite Group Databasebeta| order | 6112 |
| automorphism | ? |
| homology | Abelianization (H1) = C23 · Schur multiplier (H2) = C22 |
No aliases for this group.
| Sylow | C191 ⋊ #123 |
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C22×D191 |
| commutator, socle | C22×C191 | C23 |
| Fitting | C2×D4×C191 | C2 |
| hypercenter | C2×D4 | D191 |
| hypocenter | C191 | #123 |
| LCS | G ▷ C22×C191 ▷ C191 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
78 conjugacy classes of subgroups.
Polycyclic presentation:
2^5,191|c^2=d,b^a=bd,c^a=ce,f^c=f^190964 conjugacy classes — view the full character table.
| maximal subgroup of | #27132452, #27132454, #27132853, … |
| maximal normal subgroup of | #27132452, #27132454, #27132853, … |
| maximal quotient of | #27132524, #27132535, #27132543, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(6112, 127);